POLI 381 Data Project – Data Quality Control

Author

Adam Cheng

1 Introduction

This project aims to study how economic performance influences public approval of national governments over time. The dataset has 9 variables covering 111 countries between 1990-2023.

Table 1: A sample of the dataset (filtered by USA).
Each column represents a variable, each row represents an observation, and each cell represents a value to its corresponding variable

country_name	country_code	year	approval_smoothed	approval_growth	gdp_pc	gdp_pc_growth	unemployment_rate	cpi_growth
United States	USA	1990	53.51480	4.7219676	44378.52	NA	5.62	5.40
United States	USA	1991	56.38072	5.3553726	43742.03	-1.434248	6.82	4.23
United States	USA	1992	45.20927	-19.8143060	44659.15	2.096669	7.51	3.03
United States	USA	1993	44.96474	-0.5408824	45286.94	1.405723	6.90	2.95
United States	USA	1994	44.03471	-2.0683562	46537.36	2.761109	6.12	2.61
United States	USA	1995	43.86478	-0.3859001	47220.96	1.468929	5.65	2.81

1.1 Country Coverage

Figure 1: Map showing the dataset’s geographical coverage. Countries covered by the dataset are shaded blue and countries with no observations are coloured white

Figure 1 shows the dataset covers a wide range of countries, enhancing the external validity of the analysis.

2 Data Quality Assessment

Variables will be individually examined in concise paragraphs due to the scale of the dataset and constraints of word count.

2.1 gdp_pc

GDP per capita in 2021 PPP USD ($) from The World Bank (2025) is a covariate accounting for countries’ base income level, calculated by: $\frac{(\text{Consumption} + \text{Investment} + \text{Government Spending} - \text{Net Exports})}{\text{Population}}$ with currency converted to 2021 US purchasing power parity rates.

Table 2: Tables for gdp_pc.
Subsequent tables under this section will share the same format and comments will be kept brief

(a) Data diagnosis table. Each column represents a diagnostic metric for the variable and outliers are classified based on the 1.5 IQR rule

Variable	Type	Unique Values	Total Values	Missing Values	Missing Proportion	Outliers Count	Zero Count
gdp_pc	double	3730	3730	44	1.17	85	0

(b) Summary statistics table. Each column represents a summary statistic for the variable

Variable	Mean	Standard Deviation	Minimum	5th Percentile	25th Percentile	Median	75th Percentile	95th Percentile	Maximum
gdp_pc	23035.64	22353.66	534.81	1653.59	5936.38	14954.72	35821.23	62638.93	137821.4

(a) KDE plot of `gdp_pc` (Gaussian kenerl and a bandwidth of 2000 is used). The x-axis indicates values of the variable and the y-axis represents the proportion of data at each value, such that the area under the curve equals 1. A rug plot is provided at the bottom with each tick mark representing a value of the variable

Figure 2 suggests the distribution of gdp_pc is right-skewed with considerable variation and no notable gaps in data. Table 2 (b) supports this skewness, as the mean ($23,035.64) exceeds the median ($14,954.72), reflecting the historically substantial income disparities between countries.

2.2 gdp_pc_growth

% change of gdp_pc from the previous year derived using R, the independent variable measuring economic performance of countries over time.

Table 3: Tables for gdp_pc_growth

(a) Data diagnosis table

Variable	Type	Unique Values	Total Values	Missing Values	Missing Proportion	Outliers Count	Zero Count
gdp_pc_growth	double	3619	3619	155	4.11	281	0

(b) Summary statistics table

Variable	Mean	Standard Deviation	Minimum	5th Percentile	25th Percentile	Median	75th Percentile	95th Percentile	Maximum
gdp_pc_growth	1.96	5.53	-64.42	-6.15	0.28	2.19	4.34	8.49	90.83

(a) KDE plot for `gdp_pc_growth`. Bandwidth is set to 0.5

Figure 3 suggests gdp_pc_growth has a roughly symmetric (slight left-skew) distribution with no notable gaps in data, numerous outliers (281, Table 3 (a)), and considerable variation that reflect positive and negative economic shocks useful to the analysis.

2.3 approval_smoothed

Approval of national government (% of survey respondents) smoothed via exponential smoothing from Carlin et al. (2023) is the dependent variable measuring public approval. approval_smoothed is measured by collecting survey data from numerous sources asking respondents from countries with competitive elections whether they approve their executives.

Table 4: Tables for approval_smoothed

(a) Data diagnosis table

Variable	Type	Unique Values	Total Values	Missing Values	Missing Proportion	Outliers Count	Zero Count
approval_smoothed	double	2389	2412	1362	36.09	22	0

(b) Summary statistics table

Variable	Mean	Standard Deviation	Minimum	5th Percentile	25th Percentile	Median	75th Percentile	95th Percentile	Maximum
approval_smoothed	47.32	14.54	3.94	25.59	36.96	46.47	56.51	73.34	95.65

(a) KDE plot for `approval_smoothed`. Bandwidth is set to 2.5

Figure 4 suggests the distribution of approval_smoothed is roughly symmetric (slight right-skew) with no notable gaps in data. However, Table 4 (a) highlights rather extreme outliers and large missing data proportions (36.08%); this will be addressed later. Nonetheless, the remaining 1050 values are sufficiently large and representative for the analysis.

2.4 approval_growth

% change of approval_smoothed from the previous year derived using R, a covariate accounting for approval_smoothed’s relative changes that extends comparisons with gdp_pc_growth.

Table 5: Tables for approval_growth

(a) Data diagnosis table

Variable	Type	Unique Values	Total Values	Missing Values	Missing Proportion	Outliers Count	Zero Count
approval_growth	double	2314	2335	1439	38.13	192	22

(b) Summary statistics table

Variable	Mean	Standard Deviation	Minimum	5th Percentile	25th Percentile	Median	75th Percentile	95th Percentile	Maximum
approval_growth	2.03	24.58	-71.63	-23.47	-8.43	-0.51	7.47	34.02	455.31

(a) KDE plots for `approval_growth`. Bandwidth is set to 2

Figure 5 suggests the approval_growth distribution is right-skewed with no notable gaps in data and many extreme outliers requiring further examination. Also, Table 5 (a) reports 22 zero values, likely attributed to exponential smoothing of approval_smoothed instead of genuine stability in approval.

2.5 cpi_growth

% change of consumer price index (CPI) from the previous year from International Monetary Fund (2025), a covariate accounting for inflation. CPI measures the price level of a basket of goods and services typical households consume. The basket and its price are determined by household surveys and supplier data respectively.

Table 6: Tables for cpi_growth

(a) Data diagnosis table

Variable	Type	Unique Values	Total Values	Missing Values	Missing Proportion	Outliers Count	Zero Count
cpi_growth	double	1729	3520	254	6.73	361	1

(b) Summary statistics table

Variable	Mean	Standard Deviation	Minimum	5th Percentile	25th Percentile	Median	75th Percentile	95th Percentile	Maximum
cpi_growth	31.3	452.84	-16.12	-0.2	1.96	4.13	8.88	36.82	23773.13

(a) KDE plot for `cpi_growth`. Default bandwidth by R is applied.

Figure 6 (b) indicates an extreme outlier (Congo during its civil war in 1994) flattening the distribution. Logarithmic transformation is required.

(a) KDE plot for `cpi_growth_log10`. Bandwidth is set to 0.05

Following the transformation in Figure 7, the distribution is right-skewed with no notable gaps in data. Figure 7 (b) also reveals many outliers with greater concentration in the right tail, reflecting the historical tendencies for inflationary crises.

2.6 unemployment_rate

Unemployment rate (% of labour force) from International Monetary Fund (2025), a covariate accounting for unemployment. The variable is measured using labour force surveys, where respondents without work but available and actively seeking work are considered unemployed.

Table 7: Tables for unemployment_rate

(a) Data diagnosis table

Variable	Type	Unique Values	Total Values	Missing Values	Missing Proportion	Outliers Count	Zero Count
unemployment_rate	double	1388	2755	1019	27	156	0

(b) Summary statistics table

Variable	Mean	Standard Deviation	Minimum	5th Percentile	25th Percentile	Median	75th Percentile	95th Percentile	Maximum
unemployment_rate	8.29	5.77	0.04	2.08	4.39	6.84	10.31	19.71	38.8

(a) KDE plot for `unemployment_rate`. Bandwidth is set to 0.7

Figure 8 suggests the unemployment_rate distribution is right-skewed with no notable gaps in data, many outliers and a heavier right tail, reflecting numerous historically high unemployment crises. Table 7 (a) reports 27% missing proportions, which consistently fluctuates over time as highlighted by Figure 9, likely due to irregular survey frequencies.

2.7 Visualizing Missingness

Figure 9: Proportion of missing data for each variable (y-axis) over time (x-axis). Dervied variables are omitted because they share the same missingness patterns as their source variable

Figure 9 suggests approval_smoothed has the most missing data over time, which will be further explored in Figure 10. Missingness for other variables is negligible.

Figure 10: Heatmap of missing `approval_smoothed` values by country (y-axis) and year (x-axis). Blue squares indicate missing values and white squares indicate observed values. Countries are grouped by quartiles of their mean `gdp_pc` between 1990-2023

Figure 10 suggests missing approval_smoothed data correlates with countries’ gdp_pc, with higher-income countries generally exhibiting less missing data overall—likely due to greater resource capacity for data collection. However, missing data still declined for all countries over time, suggesting confounders like technological advancements likely reduced the cost of survey administration for all countries over time. Other factors, like warfare, can also affect data availability. Recent missing data may reflect delayed data reports as they vary by survey source.

3 Independent and Dependent Variable Relationship Assessment

3.1 Theoretical Conjecture

Denoting Variables:

Independent variable ( $X$ ): % change of GDP per capita in 2021 PPP USD from the previous year (gdp_pc_growth).
Dependent variable ( $Y$ ): Approval of national government smoothed via exponential smoothing (approval_smoothed).

Relationship Rationale:

$X$ is often assumed to be positively correlated with $Y$ because economic performance is a core responsibility of the government that impacts the living standards, happiness, and even survival of the individuals who dictate public approval of their government. Furthermore, individuals often associate their financial hardships with poor governance regardless of whether the government is directly responsible.

Necessary Considerations:

Non-linearity: The relationship between $X$ and $Y$ may not be strictly linear because it can reach a threshold—similar to a concave utility function—where further economic development produces diminishing returns of approval as individuals substitute to other concerns responsible by the government. Potential solutions to address this include
- Non-linear regression (e.g. Lowess): Visualizes non-linear patterns on scatter plots.
- Variable transformation (e.g. logarithmic, exponential): Reduces non-linearity, simpler relationship assessment.
Endogeneity: Occurs when the relationship between $X$ and $Y$ is confounded by unexplained variables influencing $Y$ . Omitting these variables from the analysis can result in misleading conclusions about the bivariate relationship. To address this omitted variable bias, I included covariates in the dataset to control for alternative explanations.
Confounds: Changes in $Y$ may not be solely due to $X$ , confounders such as cpi_growth or unemployment_rate may also influence $Y$ or both $X$ and $Y$ .
- Consider gdp_pc (more confounds explored in stage 6): The correlation between XX and YY may be weaker for high-gdp_pc countries because economic performance matters to individuals less compared to those in low-gdp_pc countries. To address this, I will
  1. Group by countries then calculate for the mean gdp_pc,
  2. Stratify countries into intervals of mean gdp_pc (e.g. quartiles),
  3. Run regressions for $X$ and $Y$ in each stratum and analyze changes in correlation using necessary metrics and visualizations.

3.2 Graphical Examination

This section will thoroughly examine the underlying distributions between $X$ and $Y$ using visualizations.

Figure 11: KDE plot of `gdp_pc_growth` and `approval_smoothed` z-scores (ensures a comparable scale) using a bandwidth of 0.15. Rug plots color-coded and separated by variable are added at the bottom, with tick marks representing values

Figure 11 indicates both variables share similar distribution shapes, i.e., unimodal and roughly symmetric. While $Y$ appears more spread out overall and $X$ is more concentrated at its centre, the rug plots reveal $X$ exhibiting a wider range with more extreme outliers on both ends.

(a) Q-Q plot for `gdp_pc_growth` and `approval_smoothed` with default axes limits

Figure 12 reveals that while the centres of both distributions are similar (roughly following the red reference line), there are substantial deviations in the tails. Specifically, an S-shaped pattern is observed with noticeable “plateaus” at the extremes ( $Y$ quantiles increasing slower than $X$ quantiles), suggesting $Y$ has a heavier tail and extreme cases occur more consistently. However, $X$ quantiles span a wider range, indicating higher extremes. The consistency of extreme $Y$ values may suggest measurement validity issues.

Since $Y$ relies on survey data, concerns about measurement are reasonable. Specifically, the consistency of extreme cases can stem from non-random selection of survey respondents. While all survey sources used by Carlin et al. (2023) are reputable (e.g. Gallup World Poll, Eurobarometer), they utilize voluntary surveys that naturally invite biases. Some biases include voluntary response bias, where individuals with stronger opinions respond more often (leading to extreme cases), and non-response bias, where individuals not responding—often with different beliefs—lack representation in the sample.

Despite these prevalent biases, Carlin et al. (2023) draw from a wide range of survey sources, offering a larger sample and reducing sampling variability, which helps to mitigate these biases. Winsorization could be a solution to further reduce the effects of biases from $Y$ and extreme outliers from $X$ by replacing extreme values with percentile values (e.g. 5th and 95th percentile) to constrain the data within a more realistic range. Figure 13 shows how Figure 12 is altered after a 90% winsorization on $X$ and $Y$ ,

Figure 13: Q-Q plot of `gdp_pc_growth` and `approval_smoothed` z-scores after 90% winsorization. Axes limits are set to (-2.5, 2.5) with no data points beyond the limit

effectively “trimming” the tails that initially produced the S pattern and emphasizing the middle quantiles following the reference line instead. Although winsorization can reduce the impact of outliers, it suffers from a trade-off of omitting potentially meaningful outliers for simplicity.

Figure 14: Line plot for z-scores of mean `gdp_pc_growth` and `approval_smoothed` for all countries across time. Standardization ensures variables are on comparable scales and fluctuations in values can be easily observed

Figure 14 indicates that $X$ and $Y$ fluctuate over time, with extreme shifts accurately reflecting major global events (e.g. COVID). $Y$ appears to follow the trend of $X$ but with a lag of ~3-4 years. The observed lag may arise from irregular survey administration frequencies creating temporal gaps between shocks to $X$ and recording of $Y$ , distorting the immediate effects between the variables. Delays in economic shocks impacting public perception may also contribute to the lag: while $X$ can easily quantify immediate economic changes, $Y$ operates in different scales as respondents vary in their tolerance and optimism for the government, often leading to a delayed change in their attitude as they observe how their government handles economic shocks.

The lagged relationship will be explored in stage 6 by accounting for lagged $X$ values by intervals of years ( $t$ ) when running regression models (e.g. distributed lag and autoregressive models).

Figure 15: Line plots for z-scores of mean `gdp_pc_growth` and `approval_smoothed` for all countries across time. Plots are separated by lagged variants of `gdp_pc_growth`

Figure 15 indicates $X_{t-1}$ , $X_{t-2}$ , $X_{t-3}$ , and $X_{t-4}$ all better overlap with $Y_t$ than $X_t$ , indicating they may better explain $Y_t$ and should be explored further as independent variables when running regressions.

4 Conclusion

While current evidence suggests a weak but evident correlation between $X$ and $Y$ , accounting for non-linearity and controlling for confounds may reveal stronger relationships. However, it is vital to first address underlying issues with $Y$ —such as lag and non-random sampling biases—to ensure the analysis avoids the perils of “garbage in, garbage out”.

References

Carlin, R. E., Hartlyn, J., Hellwig, T., Love, G. J., Martı́nez-Gallardo, C., Singer, M. M., … Sert, H. (2023). Executive Approval Database 3.0. Retrieved from https://executiveapproval.org/

International Monetary Fund. (2025). International Financial Statistics (IFS). Retrieved from https://data.imf.org/?sk=4c514d48-b6ba-49ed-8ab9-52b0c1a0179b

The World Bank. (2025). World Development Indicators. Retrieved from https://datacatalog.worldbank.org/search/dataset/0037712/World-Development-Indicators